WASHINGTON (CNN) --President Bush on Sunday said the capture of toppled Iraqi leader Saddam Hussein was good news for the Iraqi people.

"Now he will face the justice he denied to millions," Bush said during a five-minute formal television address.

"For the vast majority of Iraqi citizens who wish to live as free men and women, this event brings further assurance that the torture chambers and the secret police are gone forever," Bush said.

"This afternoon I have a message for the Iraqi people: You will not have to fear the rule of Saddam Hussein ever again," Bush said, adding a warning. "The capture of Saddam Hussein does not mean the end of violence in Iraq." (Full transcript)

The president also congratulated the U.S. military for its successful mission.

Bush also called Australian Prime Minister John Howard, Italian Prime Minister Silvio Berlusconi, and Polish President Aleksander Kwasniewski. Bush is expected to speak with Japanese Prime Minister Junichiro Koizumi on Monday.

The president also talked by phone with Senate Majority Leader Bill Frist, R-Tennessee, Sen. Minority Leader Tom Daschle, D-South Dakota, and House Speaker Dennis Hastert, R-Illinois. He was not able to reach House Minority Leader Nancy Pelosi, D-California, according to a White House spokesman.

Bush also called U.S. Army Gen. John Abizaid to congratulate him and his troops for carrying out the mission that led to Saddam's capture as well as Adnan Pachachi, the current president of the Iraqi Governing Council.

The president was first informed about the operation at about 3:15 p.m. Saturday at Camp David by Defense Secretary Donald Rumsfeld.

Rumsfeld started the phone conversation with Bush by cautioning the president that first reports are not always accurate.

Then, according to McClellan, the president said to Rumsfeld that it sounded like he was about to hear good news.

Rumsfeld then told Bush that Abizaid had called to say he was fairly confident Saddam had been captured.

"Well that is good news," the president responded, according to his spokesman.

The president and Rumsfeld discussed the need to be cautious with the information until it was confirmed because the captured man could be an impostor.

Bush also said the information should be announced from "the theater" because it was a "military matter."

Rumsfeld called the president back a short while later to express more confidence the man in custody was Saddam, because Abizaid said there were identifying marks on his body.

The president then called to inform Vice President Dick Cheney and National Security Adviser Condoleezza Rice, who then called Secretary of State Colin Powell, CIA Director George Tenet and White House Chief of Staff Andy Card.

At about 5 a.m. ET Sunday, Iraq's Civil Administrator Paul Bremer called Rice to confirm it was in fact Saddam who was in custody.

Rice then called Bush, who was now back at the White House and in the residence, at about 5:14 a.m.

Later, the president and first lady Laura Bush watched a television broadcast from Baghdad when Bremer and U.S. Army Gen. Ricardo Sanchez announced Saddam's capture, and was "particularly moved to see the outbursts of joy from Iraqi journalists," McClellan said.